Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces - D. R. Sahu; Ngai-Ching Wong; Jen-Chih Yao (Abstract and Applied Analysis)
Let be a real reflexive Banach space with a weakly continuous duality mapping . Let be a nonempty weakly closed star-shaped (with respect to ) subset of . Let  =  be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of , which is uniformly continuous at zero. We will show that the implicit iteration scheme: , for all , converges strongly to a common fixed point of the semigroup for some suitably chosen parameters and . Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009).